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34 questions tagged with cotangent.
If \(\cot x=3\), what is the value of \(\cosec^2 x\)?
B. (10)
We know \(\cosec^2 x=1+\cot^2 x\). Hence (1+9=10).
The correct answer is B. (10). We know \(\cosec^2 x=1+\cot^2 x\). Hence (1+9=10).
\(\cosec^2 x=1+\cot^2 x\) होता है। इसलिए (1+9=10) है।
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What is (\cot\left\(\frac{\pi}{2}-\theta\right\)) equal to?
D. \(\tan \theta\)
At \( \frac{\pi}{2}-\theta\), cotangent changes to the co-function tangent. In exams remember reciprocal function pairs.
The correct answer is D. \(\tan \theta\). At \( \frac{\pi}{2}-\theta\), cotangent changes to the co-function tangent. In exams remember reciprocal function pairs.
\(\frac{\pi}{2}-\theta\) पर cotangent का co-function tangent होता है। परीक्षा में reciprocal function pair याद रखें।
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What is \(\frac{1}{\cosec x-\cot x}\) equal to?
C. \(\cosec x+\cot x\)
Since (\(\cosec x-\cot x\)\(\cosec x+\cot x\)=1). Hence the required reciprocal is \(\cosec x+\cot x\).
The correct answer is C. \(\cosec x+\cot x\). Since (\(\cosec x-\cot x\)\(\cosec x+\cot x\)=1). Hence the required reciprocal is \(\cosec x+\cot x\).
क्योंकि (\(\cosec x-\cot x\)\(\cosec x+\cot x\)=1)। इसलिए आवश्यक व्युत्क्रम \(\cosec x+\cot x\) है।
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If \(\cosec x+\cot x=4\), what is the value of \(\cot x\)?
B. \(\frac{15}{8}\)
\(\cosec x-\cot x=\frac{1}{4}\). Subtracting gives \(2\cot x=4-\frac{1}{4}\), so \(\cot x=\frac{15}{8}\).
The correct answer is B. \(\frac{15}{8}\). \(\cosec x-\cot x=\frac{1}{4}\). Subtracting gives \(2\cot x=4-\frac{1}{4}\), so \(\cot x=\frac{15}{8}\).
\(\cosec x-\cot x=\frac{1}{4}\) होगा। घटाने पर \(2\cot x=4-\frac{1}{4}\), इसलिए \(\cot x=\frac{15}{8}\)।
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If \(\sin x-\cos x=\frac{1}{3}\), what is the value of \(\tan x+\cot x\)?
A. \(\frac{9}{4}\)
Squaring gives \(1-2\sin x\cos x=\frac{1}{9}\). Thus \(\sin x\cos x=\frac{4}{9}\) and \(\tan x+\cot x=\frac{9}{4}\).
The correct answer is A. \(\frac{9}{4}\). Squaring gives \(1-2\sin x\cos x=\frac{1}{9}\). Thus \(\sin x\cos x=\frac{4}{9}\) and \(\tan x+\cot x=\frac{9}{4}\).
वर्ग करने पर \(1-2\sin x\cos x=\frac{1}{9}\) मिलता है। इसलिए \(\sin x\cos x=\frac{4}{9}\) और \(\tan x+\cot x=\frac{9}{4}\)।
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If \(\sin x+\cos x=\frac{7}{5}\), what is the value of \(\tan x+\cot x\)?
B. \(\frac{25}{12}\)
Squaring gives \(1+2\sin x\cos x=\frac{49}{25}\), so \(\sin x\cos x=\frac{12}{25}\). Now \(\tan x+\cot x=\frac{1}{\sin x\cos x}=\frac{25}{12}\).
The correct answer is B. \(\frac{25}{12}\). Squaring gives \(1+2\sin x\cos x=\frac{49}{25}\), so \(\sin x\cos x=\frac{12}{25}\). Now \(\tan x+\cot x=\frac{1}{\sin x\cos x}=\frac{25}{12}\).
वर्ग करने पर \(1+2\sin x\cos x=\frac{49}{25}\), इसलिए \(\sin x\cos x=\frac{12}{25}\)। अब \(\tan x+\cot x=\frac{1}{\sin x\cos x}=\frac{25}{12}\)।
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If \(\cot x=\frac{3}{2}\), what is the value of \(\frac{\cot^2 x-1}{\cot^2 x+1}\)?
A. \(\frac{5}{13}\)
Substitute \(\cot^2 x=\frac{9}{4}\) and simplify. The value is \(\frac{\frac{9}{4}-1}{\frac{9}{4}+1}=\frac{5}{13}\).
The correct answer is A. \(\frac{5}{13}\). Substitute \(\cot^2 x=\frac{9}{4}\) and simplify. The value is \(\frac{\frac{9}{4}-1}{\frac{9}{4}+1}=\frac{5}{13}\).
\(\cot^2 x=\frac{9}{4}\) रखकर सरल करें। मान \(\frac{\frac{9}{4}-1}{\frac{9}{4}+1}=\frac{5}{13}\) है।
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What is the simplified value of (\sin-2 x\(1+\cot^2 x\))?
B. (1)
Since \(1+\cot^2 x=\cosec^2 x\). Therefore, \(\sin^2 x\cosec^2 x=1\).
The correct answer is B. (1). Since \(1+\cot^2 x=\cosec^2 x\). Therefore, \(\sin^2 x\cosec^2 x=1\).
क्योंकि \(1+\cot^2 x=\cosec^2 x\)। इसलिए \(\sin^2 x\cosec^2 x=1\) होगा।
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What is the simplified value of \(\frac{\cosec x}{\cot x}\)?
B. \(\sec x\)
Put \(\cosec x=\frac{1}{\sin x}\) and \(\cot x=\frac{\cos x}{\sin x}\). The ratio becomes \(\frac{1}{\cos x}=\sec x\).
The correct answer is B. \(\sec x\). Put \(\cosec x=\frac{1}{\sin x}\) and \(\cot x=\frac{\cos x}{\sin x}\). The ratio becomes \(\frac{1}{\cos x}=\sec x\).
\(\cosec x=\frac{1}{\sin x}\) और \(\cot x=\frac{\cos x}{\sin x}\) रखें। अनुपात \(\frac{1}{\cos x}=\sec x\) होगा।
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What is the simplified value of \(\frac{\tan x+\cot x}{\sec x\cosec x}\)?
A. (1)
\(\tan x+\cot x=\frac{1}{\sin x\cos x}\) and \(\sec x\cosec x=\frac{1}{\sin x\cos x}\). Hence the ratio is (1).
The correct answer is A. (1). \(\tan x+\cot x=\frac{1}{\sin x\cos x}\) and \(\sec x\cosec x=\frac{1}{\sin x\cos x}\). Hence the ratio is (1).
\(\tan x+\cot x=\frac{1}{\sin x\cos x}\) और \(\sec x\cosec x=\frac{1}{\sin x\cos x}\) होता है। इसलिए अनुपात (1) है।
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What is the simplified value of (\frac{\cos\(2\pi-x\)}{\sin\(\pi+x\)})?
B. -\(\cot x\)
(\cos\(2\pi-x\)=\cos x) and (\sin\(\pi+x\)=-\sin x). Hence the value is \(-\cot x\).
The correct answer is B. -\(\cot x\). (\cos\(2\pi-x\)=\cos x) and (\sin\(\pi+x\)=-\sin x). Hence the value is \(-\cot x\).
(\cos\(2\pi-x\)=\cos x) और (\sin\(\pi+x\)=-\sin x) है। इसलिए मान \(-\cot x\) है।
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What is (\tan\(\frac{3\pi}{2}+x\)) equal to?
C. -\(\cot x\)
At \(\frac{3\pi}{2}+x\), \(\tan\) changes to \(\cot\) with a negative sign. Hence (\tan\(\frac{3\pi}{2}+x\)=-\cot x).
The correct answer is C. -\(\cot x\). At \(\frac{3\pi}{2}+x\), \(\tan\) changes to \(\cot\) with a negative sign. Hence (\tan\(\frac{3\pi}{2}+x\)=-\cot x).
\(\frac{3\pi}{2}+x\) पर \(\tan\) बदलकर \(\cot\) होता है और चिन्ह ऋणात्मक है। इसलिए (\tan\(\frac{3\pi}{2}+x\)=-\cot x)।
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What is \(\frac{1+\cos x}{\sin x}\) equal to?
C. \(\cot \frac{x}{2}\)
The standard half-angle form is \(\cot \frac{x}{2}=\frac{1+\cos x}{\sin x}\). Keep the forms of \(\tan \frac{x}{2}\) and \(\cot \frac{x}{2}\) separate.
The correct answer is C. \(\cot \frac{x}{2}\). The standard half-angle form is \(\cot \frac{x}{2}=\frac{1+\cos x}{\sin x}\). Keep the forms of \(\tan \frac{x}{2}\) and \(\cot \frac{x}{2}\) separate.
मानक अर्ध-कोण रूप \(\cot \frac{x}{2}=\frac{1+\cos x}{\sin x}\) है। \(\tan \frac{x}{2}\) और \(\cot \frac{x}{2}\) के रूप अलग रखें।
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If \(\cosec x+\cot x=6\), what is the value of \(\cosec x-\cot x\)?
A. \(\frac{1}{6}\)
The identity is (\(\cosec x+\cot x\)\(\cosec x-\cot x\)=1). Therefore, the required value is \(\frac{1}{6}\).
The correct answer is A. \(\frac{1}{6}\). The identity is (\(\cosec x+\cot x\)\(\cosec x-\cot x\)=1). Therefore, the required value is \(\frac{1}{6}\).
(\(\cosec x+\cot x\)\(\cosec x-\cot x\)=1) होता है। इसलिए आवश्यक मान \(\frac{1}{6}\) है।
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If \(\tan x+\cot x=5\), what is the value of \(\tan^2 x+\cot^2 x\)?
B. (23)
(\(\tan x+\cot x\)2=\tan-2 x+\cot-2 x+2). Therefore, the value is (25-2=23).
The correct answer is B. (23). (\(\tan x+\cot x\)2=\tan-2 x+\cot-2 x+2). Therefore, the value is (25-2=23).
(\(\tan x+\cot x\)2=\tan-2 x+\cot-2 x+2) होता है। इसलिए मान (25-2=23) है।
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What is the simplified value of \(\frac{1+\tan^2 x}{1+\cot^2 x}\)?
A. \(\tan^2 x\)
The numerator is \(1+\tan^2 x=\sec^2 x\) and the denominator is \(1+\cot^2 x=\cosec^2 x\). Their ratio is \(\frac{\sec^2 x}{\cosec^2 x}=\tan^2 x\).
The correct answer is A. \(\tan^2 x\). The numerator is \(1+\tan^2 x=\sec^2 x\) and the denominator is \(1+\cot^2 x=\cosec^2 x\). Their ratio is \(\frac{\sec^2 x}{\cosec^2 x}=\tan^2 x\).
ऊपर \(1+\tan^2 x=\sec^2 x\) और नीचे \(1+\cot^2 x=\cosec^2 x\) है। अनुपात \(\frac{\sec^2 x}{\cosec^2 x}=\tan^2 x\) होता है।
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What is the simplified value of \(\frac{\cosec^2 x-1}{\cot^2 x}\)?
C. (1)
\(\cosec^2 x-1=\cot^2 x\). Hence the ratio is (1).
The correct answer is C. (1). \(\cosec^2 x-1=\cot^2 x\). Hence the ratio is (1).
\(\cosec^2 x-1=\cot^2 x\) होता है। इसलिए अनुपात (1) है।
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If (x) is in the second quadrant and \(\cot x=-\frac{3}{4}\), what is the value of \(\cosec x\)?
A. \(\frac{5}{4}\)
From \(\cosec^2 x=1+\cot^2 x\), \(|\cosec x|=\frac{5}{4}\). In the second quadrant, \(\cosec x\) is positive.
The correct answer is A. \(\frac{5}{4}\). From \(\cosec^2 x=1+\cot^2 x\), \(|\cosec x|=\frac{5}{4}\). In the second quadrant, \(\cosec x\) is positive.
\(\cosec^2 x=1+\cot^2 x\) से \(|\cosec x|=\frac{5}{4}\) मिलता है। दूसरे चतुर्थांश में \(\cosec x\) धनात्मक होता है।
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What is (\tan\(\frac{\pi}{2}+x\)) equal to?
A. \(-\cot x\)
At \(\frac{\pi}{2}+x\), \(\tan\) changes to \(\cot\) with a negative sign. Hence (\tan\(\frac{\pi}{2}+x\)=-\cot x).
The correct answer is A. \(-\cot x\). At \(\frac{\pi}{2}+x\), \(\tan\) changes to \(\cot\) with a negative sign. Hence (\tan\(\frac{\pi}{2}+x\)=-\cot x).
\(\frac{\pi}{2}+x\) पर \(\tan\) बदलकर \(\cot\) होता है और चिन्ह ऋणात्मक होता है। इसलिए (\tan\(\frac{\pi}{2}+x\)=-\cot x)।
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If \(\cot x=\frac{5}{12}\) and (x) is in the first quadrant, what is the value of \(\cos x\)?
C. \(\frac{5}{13}\)
For \(\cot x=\frac{5}{12}\), take adjacent as (5) and opposite as (12). The hypotenuse is (13), so \(\cos x=\frac{5}{13}\).
The correct answer is C. \(\frac{5}{13}\). For \(\cot x=\frac{5}{12}\), take adjacent as (5) and opposite as (12). The hypotenuse is (13), so \(\cos x=\frac{5}{13}\).
\(\cot x=\frac{5}{12}\) में आसन्न (5) और सामने (12) मानें। कर्ण (13) होगा, इसलिए \(\cos x=\frac{5}{13}\)।
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If \(\cos x=\frac{8}{17}\) and (x) is in the first quadrant, what is the value of \(\cot x\)?
A. \(\frac{8}{15}\)
\(\sin x=\frac{15}{17}\) and \(\cot x=\frac{\cos x}{\sin x}\). Therefore, \(\cot x=\frac{8}{15}\).
The correct answer is A. \(\frac{8}{15}\). \(\sin x=\frac{15}{17}\) and \(\cot x=\frac{\cos x}{\sin x}\). Therefore, \(\cot x=\frac{8}{15}\).
\(\sin x=\frac{15}{17}\) मिलता है और \(\cot x=\frac{\cos x}{\sin x}\) होता है। इसलिए \(\cot x=\frac{8}{15}\)।
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If \(\cot x=\frac{8}{15}\) and (x) is in the first quadrant, what is the value of \(\cosec x\)?
B. \(\frac{17}{15}\)
From \(\cosec^2 x=1+\cot^2 x\), \(\cosec x=\frac{17}{15}\). Take the positive value in the first quadrant.
The correct answer is B. \(\frac{17}{15}\). From \(\cosec^2 x=1+\cot^2 x\), \(\cosec x=\frac{17}{15}\). Take the positive value in the first quadrant.
\(\cosec^2 x=1+\cot^2 x\) से \(\cosec x=\frac{17}{15}\) मिलता है। प्रथम चतुर्थांश में धनात्मक मान लें।
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Where is \(\cot x\) undefined?
B. \(\sin x=0\)
\(\cot x=\frac{\cos x}{\sin x}\), so it is undefined when \(\sin x=0\). Always check the denominator carefully.
The correct answer is B. \(\sin x=0\). \(\cot x=\frac{\cos x}{\sin x}\), so it is undefined when \(\sin x=0\). Always check the denominator carefully.
\(\cot x=\frac{\cos x}{\sin x}\) है, इसलिए \(\sin x=0\) पर यह अपरिभाषित होता है। हर को हमेशा ध्यान से देखें।
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What is the period of the function \(\cot x\)?
A. \(\pi\)
\(\cot x\) repeats its value after every \(\pi\). Both \(\tan x\) and \(\cot x\) have period \(\pi\).
The correct answer is A. \(\pi\). \(\cot x\) repeats its value after every \(\pi\). Both \(\tan x\) and \(\cot x\) have period \(\pi\).
\(\cot x\) हर \(\pi\) के बाद अपना मान दोहराता है। \(\tan x\) और \(\cot x\) दोनों का काल \(\pi\) है।
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What is (\tan\(\frac{\pi}{2}-x\)) equal to?
B. \(\cot x\)
For a complementary angle with \(\frac{\pi}{2}\), \(\tan x\) changes to \(\cot x\). Remember cofunction identities.
The correct answer is B. \(\cot x\). For a complementary angle with \(\frac{\pi}{2}\), \(\tan x\) changes to \(\cot x\). Remember cofunction identities.
\(\frac{\pi}{2}\) के पूरक कोण में \(\tan x\) बदलकर \(\cot x\) हो जाता है। पूरक पहचान याद रखें।
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What is the value of \(\cosec^2 x-\cot^2 x\)?
B. (1)
Since \(\cosec^2 x=1+\cot^2 x\), the difference is (1). This identity is linked to \(\sin^2 x+\cos^2 x=1\).
The correct answer is B. (1). Since \(\cosec^2 x=1+\cot^2 x\), the difference is (1). This identity is linked to \(\sin^2 x+\cos^2 x=1\).
क्योंकि \(\cosec^2 x=1+\cot^2 x\), अंतर (1) होगा। यह पहचान \(\sin^2 x+\cos^2 x=1\) से जुड़ी है।
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How is \(\cot x\) written in terms of \(\sin x\) and \(\cos x\)?
B. \(\frac{\cos x}{\sin x}\)
\(\cot x=\frac{\cos x}{\sin x}\). \(\tan x\) and \(\cot x\) are reciprocals of each other.
The correct answer is B. \(\frac{\cos x}{\sin x}\). \(\cot x=\frac{\cos x}{\sin x}\). \(\tan x\) and \(\cot x\) are reciprocals of each other.
\(\cot x=\frac{\cos x}{\sin x}\) होता है। \(\tan x\) और \(\cot x\) एक-दूसरे के व्युत्क्रम हैं।
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What is (\cot\(\theta+\pi\)) equal to?
A. \(\cot \theta\)
The period of \(\cot \theta\) is \(\pi\). Therefore (\cot\(\theta+\pi\)) remains \(\cot \theta\).
The correct answer is A. \(\cot \theta\). The period of \(\cot \theta\) is \(\pi\). Therefore (\cot\(\theta+\pi\)) remains \(\cot \theta\).
\(\cot \theta\) का काल \(\pi\) होता है। इसलिए (\cot\(\theta+\pi\)) का मान \(\cot \theta\) ही रहता है।
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What is (\cot\left\(\frac{\pi}{2}+\theta\right\)) equal to?
D. -\(\tan \theta\)
The cofunction of \(\cot \theta\) is \(\tan \theta\), and the sign is negative in the second quadrant. In such questions, first identify the cofunction.
The correct answer is D. -\(\tan \theta\). The cofunction of \(\cot \theta\) is \(\tan \theta\), and the sign is negative in the second quadrant. In such questions, first identify the cofunction.
\(\cot \theta\) का सह-फलन \(\tan \theta\) है और दूसरे चतुर्थांश में चिह्न ऋणात्मक होता है। ऐसे प्रश्नों में पहले सह-फलन पहचानें।
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When is \(\cot \theta\) undefined?
D. जब \(\sin \theta=0\)when \(\sin \theta=0\)
\(\cot \theta=\frac{\cos \theta}{\sin \theta}\), so it is undefined when \(\sin \theta=0\). In quotient functions, identify the denominator.
The correct answer is D. जब \(\sin \theta=0\) / when \(\sin \theta=0\). \(\cot \theta=\frac{\cos \theta}{\sin \theta}\), so it is undefined when \(\sin \theta=0\). In quotient functions, identify the denominator.
\(\cot \theta=\frac{\cos \theta}{\sin \theta}\) है इसलिए \(\sin \theta=0\) पर यह अपरिभाषित होता है। भाग वाले फलनों में हर पहचानें।
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